The following 4 Problems are based on this information

The following EXCEL output produces the analysis of variance, regression coefficients, standard errors and t-tests for a simple linear regression:

ANOVA

df

SS

MS

F

P-value

Regression

1

77272

77272

2659

.00000

Residual

16

465

29

Total

17

77737

Coefficient

Standard Error

t Stat

P-value

Intercept

41.7

2.25

18.5

.0000

X

9.6

0.19

51.6

.0000

11.

What is the most precise statement we can conclude at the =0.05 significance level with respect to the linear association between Y and X?

a) There is no association between X and Y

b) There is an association, but we cannot determine the direction

c) There is a positive associaton

d) There is a negative association

12.

Give the fitted (predicted) value when X=12.

a) 41.7 b) 9.6 c) 51.3 d) 426.6 e) 137.7

13.

Give the estimated residual standard error (deviation), S.

a) 2.25 b) 0.19 c) 5.39 d) 465 e) 29

14.

What proportion of the variation in Y was “explained” by the regression model?

a) .9940 b) .0060 c) .19 d) .0000 e) 2659

3. A realtor is interested in the determinants of home selling prices in his territory. He takes a random sample of 36 homes that have sold in this area during the past 18 months, observing: selling PRICE (Y), AREA (X1), BEDrooms (X2), BATHrooms (X3), POOL dummy (X4=1 if Yes, 0 if No), and AGE (X5). He fits the following models (predictor variables to be included in model are given for each model):